To me, the answer here is “kinda but no”. Math in its most basic level is about studying logical connections. Sometimes being able to symbolize something in notation allows inspection of logical objects otherwise unobservable - like higher dimensional objects. But there’s the whole area of mathematical logic. I think I can say Godels incompleteness/inconsistency theorem was only about axiomatic systems with no necessary connection to geometry. Mathematics loves to study logical reductions of things and geometry can certainly be left out through reductions.

There’s something of a geometry/algebra separation in mathematics, too. The last few centuries (?) have tended toward algebraic research at the exclusion of geometry. There’s even reason to believe the two types of reasoning are separated in human brains in so far as people tend to be good at one and less good at the other.